The Texans failed to ever get going in offense, with quarterback Matt Schaub throwing three interceptions, the first of which was returned for the opening touchdown of the match.
Schaub was eventually replaced in the fourth quarter, and Kubiak has warned the 32-year-old that he cannot afford to put in a similar performance again if he wants to retain his starting spot.
"It's a broken record right now. It looked the same. Hopefully, that's rock bottom tonight," Kubiak told The AP.
The Texans won their opening two matches of the season, but have since lost three on the bounce and now have a 2-3 record for the year.